neverendingbooks – Page 190

get your brain subscribed to

Published February 8, 2006 by lievenlb

In the
‘subscribe
to my brain’ post I promised to blog on how-to get your own

button up and running on your homepage. It seems rather unlikely
that I’ll ever keep that promise if I don’t do it right away. So, here
we go for a quick tour :

step 1 : set up a rudimentary
FoaF-file : read the FoaF post if
you dont know what it’s all about. The easiest way to get a simple
FoaF-file of your own is to go to the FoaF-a-matic
webpage and fill in the details you feel like broadcasting over the
web, crucial is your name and email information (for later use) but
clearly the more details you fill out and the more Friends you add the
more useful your file becomes. Click on the ‘foaf-me’ button and
copy the content created. Observe that there is no sign of my email
adress, it is encrypted in the _mbox_sha1sum_ data. Give this
file a name like _foaf.rdf_ or _myname.rdf_ and put it on
your webserver to make it accessible. Also copy your
_mbox_sha1sum_ info for later smushing.

step 2 : subscribe to online services and modify your
online-life accordingly : probably you have already a few of
these accounts, but if not, take a free subscription just for fun and
(hopefully) later usage to the following sites :

del.icio.us a social bookmarks manager
citeUlike a service to
organise your academic papers
connotea a reference management
service for scientists
bloglines a web-based personal news
aggregator
43things a
‘What do you want to do with your life?’ service
audioscrobbler a database that
tracks listening habits and does wonderful things with statistics
backpackit a ‘be better organized’ service (Update october 2017 : Tom Howard emails: “I thought I’d reach out because we’ve just updated our guide which reviews the best alternatives to Backpack. Here’s the link”
flickr an online photo management and
sharing application
technorati a Google-for-weblogs
upcoming a social event
calendar
webjay a playlist
community

So far, I’m addicted to del.icio.us and use
citeUlike but hardly any of the others (but I may come back to this
later). The great thing about these services is that you get more
value-information back if you feed more into the system. For example, if
you use del.icio.us as your ‘public’ bookmarks-file you get to
know how many other people have bookmarked the same site and you can
access their full bookmarks which often is a far more sensible way to
get at the information you are after than mindless Googling. So, whereas
I was at first a bit opposed to the exhibisionist-character of these
services (after all, anyone with web-access can have a look at
‘your’ info), I’ve learned that the ‘social’ feature of
these services can be beneficial to get the right information I want.
Hence, the hardest part is not to get an account with these services but
to adopt your surfing behavior in such a way that you maximize this
added value. And, as I mentioned before, I’m doing badly myself but hope
that things will improve…

step 3 : turn these
accounts into an OPML file : Knowing the URL of your foaf-file
and sha1-info (step 1) and your online accounts, go to the FOAF Online Account
Description Generator and feed it with your data. You will then get
another foaf-file back (save the source in a file such as
_accounts.rdf_ and put it on your webserver). Read the Lost Boy’s
posts Subscribe to my
brain and foaf:
OnlineAccount Generator for more background info. Then, use the SubscribeToMyBrain-
form to get an OPML-file out of the account.rdf file and your sha1.
Save the source as _mybrain.opml_.

step 4 :
add/delete information you want : The above method uses generic
schemes to deduce relevant RSS-data from an account name, which works
for some services, but doesn’t for all. So, if you happen to know the
URL of RSS-feeds for one of these services, you can always add it
manually to the OPML-file (or delete data you don’t want to
publish…). My own attitude is to make all public web-data
available and to leave it to the subscriber to unsubscribe those parts
of my brain (s)he is not interested in. I know there are people whoo are
mainly interested to find out whether I put another paper online, would
tolerate some weblog-posts but have no interest in my musical tast,
whereas there are others who would like me to post more on 43things,
flickr or upcoming and don’t give a damn about my mathematics…
Apart from these online subscriptions, it is also a good idea to include
additional RSS-feeds you produce, such as those of your weblog or use my
Perl
script to have your own arXiv-feeds.

step 5 : make
your ‘subscribe to my brain’-button : Now, put the
OPML-file on your webserver, put the button

on your
homepage and link it to the file. Also, add information on your site,
similar to the one I gave in my own
subscription post so that your readers know what to do when do want
to subscribe to (parts of) your brain. Finally, (and optionally though
I’d wellcome it) send me an email with your URL so that I can subscribe
(next time you’re in Antwerp I’ll buy you a beer) and for the first few
who do so and are working in noncommutative geometry and/or
noncommutative algebra, I’ll send a copy of a neverending book. Mind
you, this doesn’t apply to local people, I’m already subscribed to their
brain on a daily basis…

Meyers-Briggs INTJ

Published February 7, 2006 by lievenlb

Freewheeling on your interests may lead to interesting discoveries.
Today I wanted to add some meat to my FoaF file and discovered in the
vocabulary the foaf:meyersBriggs
tag

The foaf:myersBriggs property represents the
Myers Briggs (MBTI) approach to personality taxonomy. It is included in
FOAF as an example of a property that takes certain constrained values,
and to give some additional detail to the FOAF files of those who choose
to include it. The foaf:myersBriggs property applies only to the
foaf:Person class; wherever you see it, you can infer it is being
applied to a person.
The foaf:myersBriggs property is interesting
in that it illustrates how FOAF can serve as a carrier for various kinds
of information, without necessarily being commited to any associated
worldview. Not everyone will find myersBriggs (or star signs, or blood
types, or the four humours) a useful perspective on human behaviour and
personality. The inclusion of a Myers Briggs property doesn’t indicate
that FOAF endorses the underlying theory, any more than the existence of
foaf:weblog is an endorsement of soapboxes.

Okay, but
how to determine your MB-type (after all there are just 16 such types)?
Clearly, you can consult the official Myers-Briggs page. You
can also follow the online Test,
but by far the quickest way to determine your type is to look up the Myers-Briggs
intro. One makes four choices between 2 options (pretty obvious, at
least to me). In a few seconds it was clear to me that I had to be an
INTJ-personality. But, what does this mean? There is an excellent
page The
Personality Type Portraits explaining what kind of information is
contained in your MB-type : ISTJ – The Duty Fulfillers
ESTJ –
The Guardians
ISFJ – The Nurturers
ESFJ – The Caregivers
ISTP – The Mechanics
ESTP – The Doers
ESFP – The
Performers
ISFP – The Artists
ENTJ – The Executives
INTJ – The Scientists
ENTP – The Visionaries
INTP – The
Thinkers
ENFJ – The Givers
INFJ – The Protectors
ENFP
– The Inspirers
INFP – The Idealists
This may look like a
self-fulfilling phrophecy but I swear I didn’t know any of these types
before. Still, let’s have a look how a typical INTJ is
supposed to interact with others

Other people may have a
difficult time understanding an INTJ. They may see them as aloof and
reserved. Indeed, the INTJ is not overly demonstrative of their
affections, and is likely to not give as much praise or positive support
as others may need or desire. That doesn’t mean that he or she doesn’t
truly have affection or regard for others, they simply do not typically
feel the need to express it.

sounds familiar? Another
eye-opener

When under a great deal of stress, the INTJ
may become obsessed with mindless repetitive, Sensate activities, such
as over-drinking. They may also tend to become absorbed with minutia and
details that they would not normally consider important to their overall
goal.

Fortunately, I ended up with a common career for
my MB-type…

noncommutative topology (3)

Published February 3, 2006 by lievenlb

For
finite dimensional hereditary algebras, one can describe its
noncommutative topology (as developed in part 2)
explicitly, using results of Markus
Reineke in The monoid
of families of quiver representations. Consider a concrete example,
say

$A = \begin{bmatrix} \mathbb{C} & V \\ 0 & \mathbb{C}
\end{bmatrix}$ where $V$ is an n-dimensional complex vectorspace, or
equivalently, A is the path algebra of the two point, n arrow quiver
$\xymatrix{\vtx{} \ar@/^/[r] \ar[r] \ar@/_/[r] & \vtx{}} $
Then, A has just 2 simple representations S and T (the vertex reps) of
dimension vectors s=(1,0) and t=(0,1). If w is a word in S and T we can
consider the set $\mathbf{r}_w$ of all A-representations having a
Jordan-Holder series with factors the terms in w (read from left to
right) so $\mathbf{r}_w \subset \mathbf{rep}_{(a,b)}~A$ when there are a
S-terms and b T-terms in w. Clearly all these subsets can be given the
structure of a monoid induced by concatenation of words, that is
$\mathbf{r}_w \star \mathbf{r}_{w’} = \mathbf{r}_{ww’}$ which is
Reineke’s *composition monoid*. In this case it is generated by
$\mathbf{r}_s$ and $\mathbf{r}_t$ and in the composition monoid the
following relations hold among these two generators
$\mathbf{r}_t^{\star n+1} \star \mathbf{r}_s = \mathbf{r}_t^{\star n}
\star \mathbf{r}_s \star \mathbf{r}_t \quad \text{and} \quad
\mathbf{r}_t \star \mathbf{r}_s^{\star n+1} = \mathbf{r}_s \star
\mathbf{r}_t \star \mathbf{r}_s^{\star n}$ With these notations we can
now see that the left basic open set in the noncommutative topology
(associated to a noncommutative word w in S and T) is of the form
$\mathcal{O}^l_w = \bigcup_{w’} \mathbf{r}_{w’}$ where the union is
taken over all words w’ in S and T such that in the composition monoid
the relation holds $\mathbf{r}_{w’} = \mathbf{r}_w \star \mathbf{r}_{u}$
for another word u. Hence, each op these basic opens hits a large number
of $~\mathbf{rep}_{\alpha}$, in fact far too many for our purposes….
So, what do we want? We want to define a noncommutative notion of
birationality and clearly we want that if two algebras A and B are
birational that this is the same as saying that some open subsets of
their resp. $\mathbf{rep}$’s are homeomorphic. But, what do we
understand by *noncommutative birationality*? Clearly, if A and B are
prime Noethrian, this is clear. Both have a ring of fractions and we
demand them to be isomorphic (as in the commutative case). For this
special subclass the above noncommutative topology based on the Zariski
topology on the simples may be fine.

However, most qurves don’t have
a canonical ‘ring of fractions’. Usually they will have infinitely
many simple Artinian algebras which should be thought of as being
_a_ ring of fractions. For example, in the finite dimensional
example A above, if follows from Aidan Schofield‘s work Representations of rings over skew fields that
there is one such for every (a,b) with gcd(a,b)=1 and (a,b) satisfying
$a^2+b^2-n a b < 1$ (an indivisible Shur root for A).

And
what is the _noncommutative birationality result_ we are aiming
for in each of these cases? Well, the inspiration for this comes from
another result by Aidan (although it is not stated as such in the
paper…) Birational
classification of moduli spaces of representations of quivers. In
this paper Aidan proves that if you take one of these indivisible Schur
roots (a,b) above, and if you look at $\alpha_n = n(a,b)$ that then the
moduli space of semi-stable quiver representations for this multiplied
dimension vector is birational to the quotient variety of
$1-(a^2+b^2-nab)$-tuples of $ n \times n $-matrices under simultaneous
conjugation.

So, *morally speaking* this should be stated as the
fact that A is (along the ray determined by (a,b)) noncommutative
birational to the free algebra in $1-(a^2+b^2-nab)$ variables. And we
want a noncommutative topology on $\mathbf{rep}~A$ to encode all these
facts… As mentioned before, this can be done by replacing simples with
bricks (or if you want Schur representations) but that will have to wait
until next week.

neverendingbooks Posts

get your brain subscribed to

Meyers-Briggs INTJ

noncommutative topology (3)